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 A248096 Number of ordered trees with n edges such that non-leaf vertices at even (odd) level have an odd (even) number of children. 1
 1, 1, 0, 2, 2, 6, 14, 30, 80, 191, 482, 1253, 3178, 8370, 21908, 57861, 154262, 411724, 1106990, 2986434, 8085282, 21978895, 59905632, 163786142, 448976298, 1233655230, 3397615736, 9376447532, 25926798104, 71819992609, 199282159404, 553834902261, 1541463298372 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA G.f. g is given by g = 1 + z*h/(1-z^2*h^2), where h = 1/(1-z^2*g^2). The function h(z) is the g.f. of the companion sequence A248097. G.f. g is given by g*(1-z^2*g^2)^2-z^2*g = (1-z^2*g^2)^2 + z*(1-z-z^2*g^2). EXAMPLE a(4) = 2 because we have (i) the tree Y and (ii) 3 path-trees P joined at their endpoints (the star-tree on 4 vertices). G.f. = 1 + x + 2*x^3 + 2*x^4 + 6*x^5 + 14*x^6 + 30*x^7 + 80*x^8 + 191*x^9 + 482*x^10 + ... MAPLE eq := g = 1+z*h/(1-z^2*h^2): h := 1/(1-z^2*g^2): g := RootOf(eq, g): gser := series(g, z = 0, 35): seq(coeff(gser, z, n), n = 0 .. 32); MATHEMATICA max=40; s={}; s[n_] := s[n] = Join[s[n-1], g=Sum[a[k]*z^k, {k, 0, n}] /. s[n-1]; SolveAlways[g == Normal[Series[1+z*h/(1-z^2*h^2) /. h -> 1/(1-z^2*g^2), {z, 0, n}]], z] // First]; Table[a[n] /. s[n+1], {n, 0, max}] (* Jean-François Alcover, Dec 26 2014, translated and adapted from Maple *) CROSSREFS Cf. A248097. Sequence in context: A051890 A071109 A005310 * A002203 A300863 A278331 Adjacent sequences:  A248093 A248094 A248095 * A248097 A248098 A248099 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 25 2014 STATUS approved

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Last modified November 14 15:10 EST 2019. Contains 329126 sequences. (Running on oeis4.)